Since the adoption of the ATSC digital television (DTV) standard in 1996 in the United States, there has been an ongoing effort to improve the design of receivers built for the ATSC DTV signal. The primary obstacle that faces designers in designing receivers so that they achieve good reception is the presence of multipath interference in the channel.
The broadcast television channel is a relatively severe multipath environment due to a variety of conditions that are encountered in the channel and at the receiver. Channels are characterized by impulse responses which may be several hundreds of symbols long, so that strong interfering signals may arrive at the receiver both before and after the largest amplitude signal. In addition, the signal transmitted through the channel is subject to time varying channel conditions due to the movement of the transmitter and signal reflectors, airplane flutter, and, for indoor reception, people walking around the room. If mobile reception is desired, movement of the receiver must also be considered.
Moreover, the ATSC DTV signal uses trellis coded 8-level vestigial sideband (usually referred to as 8T-VSB or, more simply, as 8-VSB) as the modulation method. 8-VSB data symbols are real and have a signal pulse shape that is complex. Only the real part of the complex pulse shape is a Nyquist pulse. Therefore, even if there is no multipath, the imaginary part of the complex pulse shape contributes intersymbol interference (ISI) when the channel gain seen by the equalizer is not real.
Multipath and intersymbol interference adversely affect the ability of the receiver to correctly receive the symbols transmitted by the transmitter. Therefore, designers add equalizers to receivers in order to cancel the effects of multipath and intersymbol interference and thereby improve signal reception.
Because the channel is not known a priori at the receiver, the equalizer must be able to modify its response to match the channel conditions that it encounters and to adapt to changes in those channel conditions. To aid in the convergence of an adaptive equalizer to channel conditions, the field sync segment of the frame as defined in the ATSC standard may be used as a training sequence for the equalizer. But when equalization is done in the time domain, long equalizers (those having many taps) are required due to the long channel impulse responses that characterize the channel.
The original Grand Alliance receiver used an adaptive decision feedback equalizer (DFE) with 256 taps. This adaptive decision feedback equalizer was adapted to the channel using a standard least mean square (LMS) algorithm, and was trained with the field sync segment of the transmitted frame. The LMS algorithm converges quite slowly and, even with only 256 taps, does not always converge during a single training sequence. Because the field sync segment is transmitted relatively infrequently (about every 260,000 symbols), the total convergence time of this equalizer is quite long if the equalizer only adapts on training symbols prior to convergence.
Therefore, in order to adapt equalizers to follow channel variations that occur between training sequences, the addition of blind and decision directed methods to equalizers has been suggested. However, when implemented in a realistic system, these methods may require several data fields to achieve convergence, and convergence may not be achieved at all under difficult multipath conditions.
In any event, because multipath signals in the broadcast channel may arrive many symbols after the main signal, the decision feedback equalizer is invariably used in 8-VSB applications.
It has been argued that a blind decision feedback equalizer is required due to the rise in mean square error (MSE) between training sequences. However, adaptation of the trained equalizer in the simulation that supported this argument was frozen between training sequences. It is possible that a decision-directed equalizer with good tracking performance may be able to follow the channel variations tested.
Blind algorithms based on the Sato algorithm and on Godard's constant modulus algorithm (CMA) have been proposed. The error term in both of these algorithms uses a continuous blending of a decision-directed term with the blind term. This blending enables a smooth transition between the blind mode and the decision-directed mode. However, when implemented in a realistic system, these algorithms also may take several data fields to converge.
As mentioned previously, adaptive equalizers utilizing the least mean square (LMS) algorithm may converge slowly or not at all depending on the channel conditions. Convergence may be adversely affected if the input data auto-correlation matrix has a large eigenvalue spread. Also, if the decision feedback equalizer has not converged before the end of the training sequence, the shape of the objective function may change so that it includes local minima. These local minima may be caused by closed eye channel conditions and decision feedback equalizer error propagation.
The recursive least square (RLS) algorithm is well known to avoid these convergence problems. However, the recursive least square algorithm, in its basic form, requires the computationally intensive inversion of the input data auto-correlation matrix. Lattice based forms of the recursive least square algorithm avoid the need for this matrix inversion. However, the lattice based forms of the recursive least square algorithm are not easily amenable to the advantage of initialization from an initial channel impulse response (CIR) estimate, even though such an initialization may be desirable.
Recent work in reduced rank filtering has connected the multi-stage nested Wiener filter (MSNWF) of Goldstein and Reed to the conjugate gradient algorithm (CG). It has been shown that the multi-stage nested Wiener filter solves the Wiener-Hopf equations in the Krylov subspace associated with the auto-correlation matrix and the cross-correlation vector. The multi-stage nested Wiener filter is then re-formulated using the Lanczos iteration. It has also been shown that the Lanczos-based multi-stage nested Wiener filter is equivalent to the conjugate gradient algorithm. Since the multi-stage nested Wiener filter often needs few dimensions to approach the performance of the full-rank Wiener filter, the conjugate gradient algorithm is a good candidate for an adaptive equalization algorithm with fast convergence.
A description of the conjugate gradient optimization algorithm and many of its mathematical properties may be found in “An Introduction to Optimization,” by E. K. P. Chong and S. Zak, New York, N.Y., John Wiley & Sons, 1996. The algorithm described is applicable to the optimization of a fixed objective function. An excellent review of adaptive filtering with the conjugate gradient algorithm is found in “Analysis of conjugate gradient algorithms for adaptive filtering,” by P. S. Chang and A. N. Willson, Jr., vol. 48, pp. 409-418, IEEE Transactions on Signal Processing, February 2000. The mathematical richness of the algorithm relationships leads to a variety of options in the implementation of the basic conjugate gradient algorithm for minimizing a quadratic objective function. These options can be carried over to the adaptive situation to provide a number of options for implementation of the algorithm. One characteristic of the algorithm which may also be exploited is that it works directly with the correlation matrices and vectors. This characteristic makes initialization based on an initial channel impulse response straightforward, assuming information is available for this purpose.
Like lattice based forms of the recursive least square algorithm, the conjugate gradient algorithm does not require the inversion of the input data auto-correlation matrix. Another characteristic of the conjugate gradient algorithm may be exploited by recognizing that the input data auto-correlation matrix is the product of two Toeplitz matrices.
It has been known internally by assignee to use these characteristics to substantially reduce the computation load in the conjugate gradient algorithm and to even eliminate the need to form the input autocorrelation matrix. Accordingly, the improved conjugate gradient algorithm disclosed in that application may be used to achieve satisfactory convergence times for equalizers.
It has also been known internally by assignee that the conjugate gradient algorithm can be used to estimate channels. The present invention reduces the computation complexity in performing the conjugate gradient algorithm with respect to channel estimators.